Fame, consummate skill, and material success are pretty widely accepted as items belonging on the plus side of life's balance sheet. In creative art, however, they can also represent the dominance of technique over content, and the pressure from a devoted public to repeat a reassuring past. Oscar Peterson, the international jazz star who died this week at 82, often stirred up such conflicting reactions. Listeners outside the jazz cognoscenti adored him for his majestic keyboard power, his driving swing, and his love of popular melody - this week, even French president Nicolas Sarkozy declared that "one of the bright lights of jazz has gone out". Some jazz fans, however, took Peterson's remarkable story simply as the usual confirmation that nobody ever went broke playing pretty tunes very fast.

Neither of these extremes catch his essence. When I became interested in jazz in the late 1960s, he had already been big news for nearly 20 years, and a lot of people owned a Peterson album who might normally run a mile from a jazz record - and it was usually the 1962 classic Night Train, a reference to his sleeping-car attendant father's life on the Canadian Pacific Railway. I didn't much care for Peterson's cascading runs, thundering boogie riffs and glistening arpeggios in those days. I liked the rough-hewn eccentricities of Thelonious Monk's wrong-sounding chords, or Miles Davis' mysterious, private lyricism. Peterson was amazing to witness, but rather like watching somebody bicycling along a highwire. At the time it didn't sound like music to me.

Two things happened, much later, to change my mind. One was a conversation in the mid-80s with the late broadcaster, writer and musician Benny Green, in the course of researching my biography of Ronnie Scott. Green had heard a 27-year-old Peterson at the Gaumont in Kilburn in March 1953. The second world war, and a union embargo on foreign musicians, had made this star-packed show the first major UK concert appearance by American musicians since the 1930s. Peterson (a Canadian, but an American jazzer to his fingertips) had opened the show with a roaring C Jam Blues - and in that moment, Benny Green recalled, the exhilarating optimism, confidence and inspirational power of jazz seemed to wash over him in a way that it never quite had on listening to imported American records. Peterson's energy seemed to represent the inspirational spirit of jazz, and that concert and his part in it helped raise the bar for the aspirations of local players.

The second episode in my Peterson conversion came two years ago, on the pianist's concert at a packed Royal Albert Hall. He had taught himself to play again - more economically, and in some ways more eloquently - following a stroke, and though he could barely make it to the piano stool, Peterson's still-flowing lyrical invention, a startling raft of new compositions, and an undimmed love of music-making vibrated around the hall. The audience had stood as one when he came to the stage, and the gesture represented gratitude for a communicative gift Peterson had freely shared all his life. It was one of those moments where you nod to yourself and think: OK. Now I get it.